Journal of Applied Crystallography

Volume 37, Part 4 (August 2004)

research papers

J. Appl. Cryst. (2004). 37, 635-642 [ doi:10.1107/S0021889804013743 ]

High-throughput powder diffraction. III. The application of full-profile pattern matching and multivariate statistical analysis to round-robin-type data sets

G. Barr, W. Dong, C. Gilmore and J. Faber

Abstract: Powder pattern matching techniques, using all the experimentally measured data points, coupled with cluster analysis, fuzzy clustering and multivariate statistical methods are used, with appropriate visualization tools, to analyse a set of 27 powder diffraction patterns of alumina collected at seven different laboratories on different instruments as part of an International Center for Diffraction Data Grant-in-Aid program. In their original form, the data factor into six distinct clusters. However, when a non-linear shift of the form $\Delta \left({2\theta } \right)\, = \,a_0 \, + \,a_1 \sin \theta$ (where a₀ and a₁ are refinable constants) is applied to optimize the correlations between patterns, clustering produces a large 25-pattern set with two outliers. The first outlier is a synchrotron data set at a different wavelength from the other data, and the second is distinguished by the absence of K [alpha] ₂ lines, i.e. it uses Ge-monochromated incident X-rays. Fuzzy clustering, in which samples may belong to more than one cluster, is introduced as a complementary method of pinpointing problematic diffraction patterns. In contrast to the usual methodology associated with the analysis of round-robin data, this process is carried out in a routine way, with minimal user interaction or supervision, using the PolySNAP software.

Keywords: powder diffraction; pattern matching; non-parametric statistics; multivariate analysis; fuzzy clustering.